26. A distribution with of µ =38 and a standard deviation of Ï?=20 is being transformed into a standardized distribution with µ=50 and Ï? =10. Find the new, standardized score for each of the following values from the original population.

a. X = 48 b. X = 40
c. X =30 d. X = 18

2. A jar contain 20 red marbles, of which 10 are large and 10 are small, and 30 blue marbles, of which 10 are large and 20 are small. If 1 marble is randomly selected from the jar,
a. What is the probability of obtaining a blue marble?
b. What is the probability of obtaining a large marble?
c. What is the probability of obtaining a large blue marble?

12. For a normal distribution, find the z-scores values that separate
a. The middle 60% of from the distribution from the 40% in tails.
b. The middle 70% of distribution from the 30% in the tails.
c. The middle 80 % of distribution from the 20% in the tails.
d. The middle 90% of distribution from the 10% in the tails.

18. A normal distribution has a mean of µ = 80 and a standard deviation of Ï? =10. For each of the following scores, indicate whether the body of the distribution is to the left or right of the scores, and find the proportion of the distribution in the body.
a. X = 85 b. X =92
c. X= 78 c. X = 72

Solution Preview

24. The Z score corresponding to (a) is
The Z score corresponding to (b) is
Clearly (b) lead to a better grade because is greater than . This means the number of students who secured lesser marks in case (a) is greater than that of case ...